I need help with the second bullet point in d cosandsin 0simple and memorable form for the inverse.)sin 0une nonzero),(6(All but the first of these is a "special kind of matrix" and there is a090).(d) Consider the matrix M-Cos 0sin 00(13) (3) (cossin 0It is a fact that this gives counter-cos ((c) Consider the matrix M =clockwise rotation around the origin by angle 0. On the basis of this fact, thinking geomet-rically, what should the inverse matrix be? Explain how this agrees with your calculation in(b) (using elementary trigonometry).- sinsin 0- cos 0utrices:cos 0sin 0(e)Going back to (b):-• (i 3¹); is a rotation. What is the angle? Sino1123 4- sin 0Cos 0It is a fact that this is reflectionSing-Coacross a a line.. What should the inverse of a reflection be? Explain how this agrees with your answerin (b).Show that M indeed is a reflection. To do this, you need to find a (nonzero) columnvector v such that My = v, another (nonzero) column vector w such that Mw = -w, andyou need v and w to be perpendicular to each other. (This shows that M gives reflectionacross the line spanned by v, or in other words, Rv is the line of symmetry. Your job is tofind v and w.

Answered: Image /qna-images/answer/ef32058c-f011-45c1-952f-e746a21275d2.jpg

Show that M indeed is a reflection. To do this, you need to find a (nonzero) column vector v such that Mv = v, another (nonzero) column vector w such that Mw=-w, and you need v and w to be perpendicular to each other. (This shows that M gives reflection across the line spanned by v, or in other words, Rv is the line of symmetry. Your job is to find v and w.

Show that M indeed is a reflection. To do this, you need to find a (nonzero) column vector v such that Mv = v, another (nonzero) column vector w such that Mw=-w, and you need v and w to be perpendicular to each other. (This shows that M gives reflection across the line spanned by v, or in other words, Rv is the line of symmetry. Your job is to find v and w.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 24E

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